# Neutralization Dialysis for Phenylalanine and Mineral Salt Separation. Simple Theory and Experiment

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{+}form [22], or, using the enhancement factor for some model parameters, to take into account chemical reaction between components that diffuse through the IEM in opposite directions [23].

## 2. Theoretical

#### 2.1. System under Study

^{A}, V

^{B}and V

^{D}for the acid, alkali (base) and desalination one, respectively (Figure 1). The acid (HCl), alkali (NaOH) and salt (NaCl) or mixed (NaCl + Phe) solutions circulate through the compartments A, B and D, respectively, and through the intermediate tanks. It is assumed that the thickness ( $\delta $ ) of DBLs adjacent to the surfaces of CEM is equal to those adjacent to the surfaces of AEM. The thicknesses of CEM and AEM are denoted as d

^{c}and d

^{a}, respectively. This assumption is reasonable because the hydrodynamic conditions are the same in all the compartments. Besides, by setting the DBL thickness, we implicitly took into account the effect of convection, which depends on the solution velocity, and the ability of the spacer to turbulize the flow. We assumed that the concentrations of all ions practically do not change along compartment D. In other words, the ion concentrations are the same at any moment of time both in the compartment volumes and in the corresponding intermediate tanks.

_{prof}membrane (which was used in the current study) is two orders of magnitude lower than that of the salt ions. Thus, for the sake of simplicity, we assumed the constant phenylalanine concentration in the desalination circuit, i.e., there is no transport of Phe species through the membranes and adjacent diffusion layers. At the membrane/solution interfaces a local thermodynamic equilibrium was assumed between exchanging ions. In the desalination solution, we assumed local equilibrium of the protolysis reactions for amino acid and water.

#### 2.2. Problem Formulation

^{+}, OH

^{−}, Na

^{+}, Cl

^{−}; in the CEM, j = H

^{+}, Na

^{+}; in the AEM, j = OH

^{−}, Cl

^{−}.

^{±}, Phe

^{+}and Phe

^{−}, correspondently.

^{±}, Phe

^{+}and Phe

^{−}in the desalination circuit are calculated in accordance with Equations (8) and (9) as follows:

^{+}( ${J}_{H}^{(1)}$ ) and Na

^{+}( ${J}_{Na}^{(1)}$ ) ions through the interface 1 of the CEM (Figure 1) as [24]:

^{−}( ${J}_{OH}^{(4)}$ ) and Cl

^{−}( ${J}_{Cl}^{(4)}$ ) ions through the interface 4 of the AEM:

^{+}ions concentration in the D circuit is calculated using the electroneutrality condition (2), where the presence of Phe

^{+}and Phe

^{−}ions is taken into account:

^{+}/Na

^{+}exchange (interfaces 1 and 2) and ${K}^{a}$ is the equilibrium coefficient for OH

^{−}/Cl

^{−}exchange (interfaces 3 and 4).

## 3. Experiment

_{prof}) and anion-exchange (MA-40

_{prof}) membranes with a profiled surface. Detailed characteristics of the profile on the surface of studied membranes are presented in [22]. The basic characteristics of these membranes are presented in Table 1. The JSC Innovative Enterprise “Membrane Technology” (Russia) manufactured profiled membranes from flat sheets, which are produced by “Shchekinoazot” (Russia).

_{prof}and MA-40

_{prof}membranes were chosen under the assumption that the relatively large thickness of these membranes and their aromatic polymer matrix will contribute to the retention of aromatic phenylalanine in the desalination compartment while maintaining high fluxes of salt ions through CEM and AEM.

^{−1}. Both the HCl and NaOH solutions had the concentration of 0.3 mol L

^{−1}. The choice of these concentrations was based on the analysis of phenylalanine and sodium chloride separation efficiency by diffusion dialysis method [22]. The volume of solution in D circuit was 1 L, and that in A and B circuits was 2 L. The ND process was carried out in a circulating (batch) hydrodynamic mode. The solution volumetric flow velocity in each of the compartments was equal to 12 mL min

^{−1}(the corresponding linear flow velocity was 0.2 cm s

^{−1}). The calculated DBL thickness in this case was about 400 μm (Table A1, Appendix A). A higher value of the DBL thickness (than in real electrodialysis) was chosen in order to partially level the internal diffusion kinetics of the ND process, which could be due to the relatively large thickness of the membranes under study. The solutions were temperature-stabilized at 25 °C.

^{+}(CEM) and OH

^{−}(AEM) ions. All solutions were prepared using distilled water and reagents of analytic grade. The pH of the feed solutions in the experiments was equal to 5.90 ± 0.05. This value was close to the isoelectric point pI = (pK

_{1}+ pK

_{2})/2 = 5.76 [43]. As the estimates (made with the use of Equations (8) and (9) at the presented above values of K

_{1}and K

_{2}) [22] show, the zwitterion mole fraction in the model solutions varied in the range from 99.9% to 99.8% where the pH changed between 5.85 and 5.95, respectively. Thus, the phenylalanine almost completely was presented in the form of zwitterion in the initial solution.

^{+}ions was determined using the emission flame photometry.

## 4. Parameters of the Model

^{+}, Cl

^{−}, H

^{+}and OH

^{−}ions concentrations and fluxes as functions of time and the coordinate (normal to the membrane surface) in the membranes and solutions, as well as concentrations of Phe

^{±}, Phe

^{+}and Phe

^{−}in the D circuit as functions of time.

## 5. Results and Discussion

^{+}ions through CEM exceeded the flux of Cl

^{−}ions through AEM (Figure 3a) at the beginning of the ND process. Then they changed places. At the last stage of the ND process, the transfer of cations through CEM again dominated the transfer of anions through AEM. The changes in fluxes were accompanied by significant fluctuations in the pH of solution in the D compartment (Figure 4a). It means that a higher exchange rate across the CEM than that across the AEM at the beginning of the ND process (Figure 3a) led to a decrease in the pH of the desalinated solution (Figure 4a). In the next 50 min of the ND process, there was an increase in the concentration of H

^{+}ions and a decrease in the concentration of Na

^{+}ions in the D circuit. The concentrations gradients of cations in the CEM decreased, causing a decrease in cation flux (J

^{c}) through this membrane. Next, this scenario was repeated.

^{−}ions in the AEM than H

^{+}in the CEM. It is known that sulfo groups, which are fixed groups in the studied CEM, provide a high proton transfer rate [41]. This rate is noticeably higher than that for the hydroxyl ion with the participation of weakly basic fixed groups [41] in studied AEM. This is evidenced, for example, by the specific electric conductivity of MK-40 and MA-40 membranes in 0.1 M HCl and NaOH solutions, respectively. The values of this conductivity are 36 mS cm

^{−1}[44] and 6.4 mS cm

^{−1}[45], respectively. For this reason, there was a less dramatic decrease in the exchange rate (flux) across the AEM (compared to that across the CEM; Figure 3a). In addition, the achieved low pH value of the desalinated solution stimulated the increase in J

^{a}. Due to the delay in the formation of concentration profiles in the AEM and adjacent diffusion layers, the moment where the exchange rate across the AEM decreases shifted in time.

^{c}, J

^{a}(Figure 3b) and a slow increase in the value of the solution pH in the desalination compartment (Figure 4a). The increase in pH led to a slight decrease in the concentration of phenylalanine cations and an increase in concentration of its anions (Figure 4b). The concentrations of these ions turned out to be two to five orders of magnitude lower than the concentration of the zwitterionic form (Figure 4b). Therefore, the loss of amino acid in the process of ND did not exceed 1% if we assumed that all of charged Phe forms would be transported through the IEM. Similar values of amino acid loss were measured by us experimentally. This justified the assumption made in the simulation of ND that the concentration of Phe in the D circuit remained unchanged.

^{c}and J

^{a}(Figure 3b). These data were in good agreement with published data, for example [34]. As simulations show, the decrease in DBL thickness by eight times led to an increase in cations flux approximately by 1.7 times in the beginning of the ND process (Figure 3b). In a quasi-steady state (after about 100 min) the desalination rate was about two times higher than that for the DBL thickness equal to 400 microns.

^{+}cations (Figure 4b).

^{+}and Cl

^{−}ions in the desalination circuit by two times, as well as the ion transfer coefficients for CEM and AEM (k

_{i}= J

_{i}/C

_{i}). The simulations were carried out for DBL thicknesses from 50 to 400 μm. It could be seen that a decrease in DBL thickness by eight times led to a reduction in desalination time by almost 30 times in the case of Na

^{+}ions and only 1.5 times in the case of Cl

^{−}ions. The difference between the mass transfer coefficients of Na

^{+}ions through CEM and Cl

^{−}ions through AEM and, accordingly, the concentrations of these ions in the desalination circuit decreased with increasing DBL thickness. This is explained by the fact that in the case of a thick DBL, the characteristics of the ND process are mainly determined by the external diffusion kinetics. On the contrary, if the DBL thickness is small, the main role is played by the characteristics of the membranes. In this particular case, the transport characteristics of the AEM are much worse than the characteristics of the CEM. By varying the parameters of the membranes in the calculations, it is possible to find the optimal combination of their characteristics, which will ensure the same rates of extraction of salt cations and anions from the desalination circuit of the dialyzer. We planned to do such calculations and their experimental verification in the future.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Parameter | Value | Description |
---|---|---|

${D}_{H}^{c}$ | 2.7 × 10^{−6} cm^{2} s^{−1} | H^{+} and Na^{+} ions diffusion coefficients in the MK-40_{prof} |

${D}_{Na}^{c}$ | 7.88 × 10^{−7} cm^{2} s^{−1} | |

${D}_{OH}^{a}$ | 9.6 × 10^{−7} cm^{2} s^{−1} | OH^{−} and Cl^{−} ions diffusion coefficients in the MA-40_{prof} |

${D}_{Cl}^{a}$ | 3.03 × 10^{−7} cm^{2} s^{−1} | |

${d}^{a}$ and ${d}^{c}$ | 590 and 650 µm | Thickness of the MA-40_{prof} and MK-40_{prof}, respectively |

${D}_{H}^{0}$ | 9.3 × 10^{−5} cm^{2} s^{−1} | H^{+}, OH^{−}, Na^{+} and Cl^{−} ions diffusion coefficients in solution at infinite dilution |

${D}_{OH}^{0}$ | 5.3 × 10^{−5} cm^{2} s^{−1} | |

${D}_{Na}^{0}$ | 1.33 × 10^{−5} cm^{2} s^{−1} | |

${D}_{Cl}^{0}$ | 2.03 × 10^{−5} cm^{2} s^{−1} | |

${C}_{H}^{A}$ | 0.3 mmol cm^{−3} | H^{+} and OH^{−} ions initial concentrations in the A and B circuits, respectively |

${C}_{OH}^{B}$ | 0.3 mmol cm^{−3} | |

${C}_{Na}^{D}$ | 0.025 mmol cm^{−3} | Na^{+}, Cl^{−}, H^{+} and OH^{−} ions initial concentrations in the D circuit |

${C}_{Cl}^{D}$ | 0.025 mmol cm^{−3} | |

${C}_{H}^{D}$ | 10^{−5.9} mmol cm^{−3} | |

${C}_{OH}^{D}$ | 10^{−8.1} mmol cm^{−3} | |

${C}_{Phe}^{D}$ | 0.025 mmol cm^{−3} | Initial concentration of phenylalanine in the D circuit |

${X}^{c}$ | 1.7 mmol cm^{−3} | Ion-exchange capacity of the MK-40_{prof} and MA-40_{prof} |

${X}^{a}$ | 2.4 mmol cm^{−3} | |

${K}^{c,a}$ | 1.0 | Nikolskii equilibrium constant (upper indexes “c” and “a” denote the MK-40_{prof} and MA-40_{prof} membranes, respectively) |

${K}_{i}$ (i = 1,2) | ${K}_{1}$= 6.31 × 10^{−3} mol L^{−1}${K}_{2}$ = 4.90 × 10 ^{−10} mol L^{−1} | Equilibrium constants for the phenylalanine protonation/deprotonation chemical reactions in Equations (6) and (7) denoted by ( ${K}_{1}$ ) and ( ${K}_{2}$ ), respectively |

${V}^{A}$ | 2000 cm^{3} | Solution volumes in A, B and D circuits |

${V}^{B}$ | 2000 cm^{3} | |

${V}^{D}$ | 1000 cm^{3} | |

S | 7.14 cm^{2} | Working surface area of membrane |

F | 96.485 C mmol^{−1} | Faraday constant |

R | 8.314 × 10^{−3} J mmol^{−1} K^{−1} | Gas constant |

T | 298 K | Absolute temperature |

## References

- Amrane, C.; Lalmi, A.; Bouhidel, K.E. Coupling diffusion dialysis with precipitation-cementation to separate and recover nitric acid, Cu
^{++}, Zn^{++}and Pb^{++}from the wastewater of a brass pickling bath. Int. J. Glob. Warm.**2017**, 11, 337–357. [Google Scholar] - Kerr, C. Sustainable technologies for the regeneration of acidic tin stripping solutions used in PCB fabrication. Circuit World
**2004**, 30, 51–58. [Google Scholar] [CrossRef] - Luo, J.; Wu, C.; Xu, T.; Wu, Y. Diffusion dialysis-concept, principle and applications. J. Membr. Sci.
**2011**, 366, 1–16. [Google Scholar] [CrossRef] - Janiszewska, M.; Arguillarena, A.; Wajs, M.; Staszak, K.; Regel-Rosocka, M. Application of diffusion dialysis for reduction of acidity of real pregnant leach solutions containing Ni and Co ions. Sep. Sci. Technol.
**2019**. [Google Scholar] [CrossRef] - Khan, M.I.; Mondal, A.N.; Cheng, C.; Pan, J.; Emmanuel, K.; Wu, L.; Xu, T. Porous BPPO-based membranes modified by aromatic amine for acid recovery. Sep. Purif. Technol.
**2016**, 157, 27–34. [Google Scholar] [CrossRef] - Xiao, H.-F.; Chen, Q.; Cheng, H.; Li, X.M.; Qin, W.M.; Chen, B.S.; Xiao, D.; Zhang, W.M. Selective removal of halides from spent zinc sulfate electrolyte by diffusion dialysis. J. Membr. Sci.
**2017**, 537, 111–118. [Google Scholar] [CrossRef] - Noubli, A.; Akretche, D.E.; Crespo, J.G.; Velizarov, S. Complementary membrane-based processes for recovery and preconcentration of phosphate from industrial wastewater. Sep. Purif. Technol.
**2020**, 234, 116123. [Google Scholar] [CrossRef] - Skopinska-Wisniewska, J.; Olszewski, K.; Bajek, A.; Rynkiewicz, A.; Sionkowska, A. Dialysis as a method of obtaining neutral collagen gels. Mater. Sci. Eng. C
**2014**, 40, 65–70. [Google Scholar] [CrossRef] - Vasil’eva, V.I.; Goleva, E.A. Selective separation of sodium ions from a mixture with phenylalanine by Donnan dialysis with a profiled sulfogroup cation exchange membrane. Rus. J. Phys. Chem. A
**2013**, 87, 1895–1901. [Google Scholar] [CrossRef] - Stamatialis, D.F.; Papenburg, B.J.; Gironés, M.; Saiful, S.; Bettahalli, S.N.M.; Schmitmeier, S.; Wessling, M. Medical applications of membranes: Drug delivery, artificial organs and tissue engineering. J. Membr. Sci.
**2008**, 308, 1–34. [Google Scholar] [CrossRef] [Green Version] - Tijink, M.S.L.; Wester, M.; Sun, J.; Saris, A.; Bolhuis-Versteeg, L.A.M.; Saiful, S.; Joles, J.A.; Borneman, Z.; Wessling, M.; Stamatialis, D.F. A novel approach for blood purification: Mixed-matrix membranes combining diffusion and adsorption in one step. Acta Biomater.
**2012**, 8, 2279–2287. [Google Scholar] [CrossRef] [PubMed] - Yamaguchi, N.; Miyamoto, K.; Murata, T.; Ishikawa, E.; Horiuchi, T. Newly developed neutralized pH icodextrin dialysis fluid: nonclinical evaluation. Artif. Organs
**2016**, 40, E158–E166. [Google Scholar] [CrossRef] [PubMed] - Stancheva, K.A. Applications of dialysis. Oxid. Commun.
**2008**, 31, 758–775. [Google Scholar] - Radke, W. Consequences of on-line dialysis on polyelectrolyte molar masses determined by size-exclusion chromatography with light scattering detection. J. Sep. Sci.
**2016**, 39, 696–702. [Google Scholar] [CrossRef] [PubMed] - Huang, R.L.; Tan, Z.L.; Xing, T.X.; Pan, Y.F.; Li, T.J. An in vitro method for the estimation of ileal crude protein and amino acids digestibility using the dialysis tubing for pig feedstuffs. Anim. Feed Sci. Tech.
**2000**, 88, 79–89. [Google Scholar] [CrossRef] - Wijmans, J.G.; Baker, R.W. The solution-diffusion model: a review. J. Membr. Sci.
**1995**, 107, 1–21. [Google Scholar] [CrossRef] - Ring, S.; Hasson, D.; Shemer, H.; Semiat, R. Simple modeling of Donnan separation processes. J. Membr. Sci.
**2015**, 476, 348–355. [Google Scholar] [CrossRef] - Agarwal, C.; Goswami, A. Nernst Planck approach based on non-steady state flux for transport in a Donnan dialysis process. J. Membr. Sci.
**2016**, 507, 119–125. [Google Scholar] [CrossRef] - Szczepański, P.; Szczepańska, G. Donnan dialysis—A new predictive model for non−steady state transport. J. Membr. Sci.
**2017**, 525, 277–289. [Google Scholar] [CrossRef] - Szczepański, P. Chemometric method for Donnan dialysis physicochemical model simplification. Prediction of: Transport, recovery, concentration, and desalination efficiency. Desalination
**2018**, 444, 6–12. [Google Scholar] - Prado-Rubio, O.A.; Møllerhøj, M.; Jørgensen, S.B.; Jonsson, G. Modeling Donnan dialysis separation for carboxylic anion recovery. Comput. Chem. Eng.
**2010**, 34, 1567–1579. [Google Scholar] [CrossRef] - Vasil’eva, V.; Goleva, E.; Pismenskaya, N.; Kozmai, A.; Nikonenko, V. Effect of surface profiling of a cation-exchange membrane on the phenylalanine and NaCl separation performances in diffusion dialysis. Sep. Purif. Technol.
**2019**, 210, 48–59. [Google Scholar] [CrossRef] - Štěpánek, V.; Palatý, Z.; Bendová, H. Numerical analysis of dialysis with chemical reaction at steady state. Irreversible second-order reaction. Chem. Eng. Process.
**2015**, 95, 362–371. [Google Scholar] [CrossRef] - Igawa, M.; Echizenya, K.; Hayashita, T.; Seno, M. Neutralization dialysis for deionization. Bull. Chem. Soc. Jpn.
**1987**, 60, 381–383. [Google Scholar] [CrossRef] [Green Version] - Igawa, M.; Mikami, K.; Okochi, H. Transport characteristics of neutralization dialysis and desalination of tap water. Bull. Chem. Soc. Jpn.
**2003**, 76, 437–441. [Google Scholar] [CrossRef] - Bleha, M.; Tishchenko, G.A. Neutralization dialysis for desalination. J. Membr. Sci.
**1992**, 73, 305–311. [Google Scholar] [CrossRef] - Tanabe, H.; Okochi, H.; Igawa, M. Separation of weak acids and bases by neutralization dialysis. Ind. Eng. Chem. Res.
**1995**, 34, 2450–2454. [Google Scholar] [CrossRef] - Zheleznov, A.; Windmöller, D.; Körner, S.; Böddeker, K.W. Dialytic transport of carboxylic acids through an anion exchange membrane. J. Membr. Sci.
**1998**, 139, 137–143. [Google Scholar] [CrossRef] - Ueno, K.; Doi, T.; Nanzai, B.; Igawa, M. Selective transport of neutral amino acids across a double-membrane system comprising cation and anion exchange membranes. J. Membr. Sci.
**2017**, 537, 344–352. [Google Scholar] [CrossRef] - Wang, G.; Tanabe, H.; Igawa, M. Transport of glycine by neutralization dialysis. J. Membr. Sci.
**1995**, 106, 207–211. [Google Scholar] [CrossRef] - Wang, M.; Hou, S.; Liu, Y.; Xu, X.; Lu, T.; Zhao, R.; Pan, L. Capacitive neutralization deionization with flow electrodes. Electrochim. Acta
**2016**, 216, 211–218. [Google Scholar] [CrossRef] - Liu, Y.; Zhang, Y.; Ou-Yang, W.; Bastos Sales, B.; Sun, Z.; Liu, F.; Zhao, R. Capacitive neutralization dialysis for direct energy generation. Envir. Sci. Tech.
**2017**, 51, 9363–9370. [Google Scholar] [CrossRef] [PubMed] - Chérif, M.; Mkacher, I.; Ghalloussi, R.; Chaabane, L.; Ben Salah, A.; Walha, K.; Dammak, L.; Grande, D. Experimental investigation of neutralization dialysis in three-compartment membrane stack. Desalin. Water Treat.
**2015**, 56, 2567–2575. [Google Scholar] [CrossRef] - Chérif, M.; Mkacher, I.; Dammak, L.; Ben Salah, A.; Walha, K.; Grande, D.; Nikonenko, V. Water desalination by neutralization dialysis with ion-exchange membranes: Flow rate and acid/alkali concentration effects. Desalination
**2015**, 361, 13–24. [Google Scholar] [CrossRef] - Tsukahara, S.; Nanzai, B.; Igawa, M. Selective transport of amino acids across a double membrane system composed of a cation- and an anion-exchange membrane. J. Membr. Sci.
**2013**, 448, 300–307. [Google Scholar] [CrossRef] - Sato, K.; Yonemoto, T.; Tadaki, T. Modeling of ionic transport in neutralization dialytic deionization. J. Chem. Eng. Jpn.
**1993**, 26, 68–74. [Google Scholar] [CrossRef] [Green Version] - Denisov, G.A.; Tishchenko, G.A.; Bleha, M.; Shataeva, L.K. Theoretical analysis of neutralization dialysis in the three-compartment membrane cell. J. Membr. Sci.
**1995**, 98, 13–25. [Google Scholar] [CrossRef] - Chérif, M.; Korchane, S.; Chaabane, L.; Dammak, L.; Ben Salah, A.; Walha, K.; Kozmai, A. Reconstituted and brackish waters desalination by neutralization dialysis process with ion-exchange membranes. Desalin. Water Treat.
**2017**, 65, 52–59. [Google Scholar] [CrossRef] - Kozmai, A.; Chérif, M.; Dammak, L.; Bdiri, M.; Larchet, C.; Nikonenko, V. Modelling non-stationary ion transfer in neutralization dialysis. J. Membr. Sci.
**2017**, 540, 60–70. [Google Scholar] [CrossRef] - Lide, D.R. Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, USA, 2005; ISBN 0849304873. [Google Scholar]
- Zabolotskii, V.I.; Loza, S.A.; Sharafan, M.V. Physicochemical properties of profiled heterogeneous ion-exchange membranes. Russ. J. Electrochem.
**2005**, 41, 1053–1060. [Google Scholar] [CrossRef] - Berezina, N.P.; Kononenko, N.A.; Dyomina, O.A.; Gnusin, N.P. Characterization of ion-exchange membrane materials: Properties vs structure. Adv. Colloid Interfac.
**2008**, 139, 3–28. [Google Scholar] [CrossRef] [PubMed] - Vermaas, D.A.; Kunteng, D.; Saakes, M.; Nijmeijer, K. Fouling in reverse electrodialysis under natural conditions. Water Res.
**2013**, 47, 1289–1298. [Google Scholar] [CrossRef] [PubMed] - Gnusin, N.P.; Karpenko, L.V.; Demina, O.A.; Berezina, N.P. Calculation of the ion-exchange equilibrium constant for MK-40 sulfo cation-exchange membranes from conductometric data. Rus. J. Phys. Chem.
**2001**, 75, 1550–1554. [Google Scholar] - Kozmai, A.E.; Nikonenko, V.V.; Zyryanova, S.; Pismenskaya, N.D.; Dammak, L.; Baklouti, L. Modelling of anion-exchange membrane transport properties with taking into account the change in exchange capacity and swelling when varying bathing solution concentration and pH. J. Membr. Sci.
**2019**, 590, 117291. [Google Scholar] [CrossRef] - Sousa, P.; Soares, A.; Monteiro, E.; Roubo, A. A CFD study of the hydrodynamics in a desalination membrane filled with spacers. Desalination
**2014**, 349, 22–30. [Google Scholar] [CrossRef]

**Figure 1.**Scheme of the laboratory cell (

**a**) and the modeled system geometry (

**b**). In (

**a**): the acid, saline and alkaline solutions circuits are denoted as 1, 2 and 3, respectively; 4 is the peristaltic pumps. In (

**b**) DBL1 and DBL2 are the diffusion boundary layers adjacent to the cation exchange membrane (CEM) from the sides of A and D compartments, respectively; DBL3 and DBL4 are the diffusion boundary layers adjacent to the anion exchange membrane (AEM) from the sides of D and B compartments, respectively; the numbers 1, 2, 3 and 4 indicate the interfaces of the CEM and AEM with the corresponding compartments.

**Figure 2.**The molar fractions ( $\alpha $) of phenylalanine species in aqueous solutions as function of pH calculated using Equations (5)–(8), (9).

**Figure 3.**Time dependencies of Na

^{+}ions flux (J

^{c}) across the CEM and Cl

^{−}ions flux (J

^{a}) across the AEM from the D compartment into A and B compartments, respectively, in the course of neutralization dialysis (ND) of individual NaCl solution (

**a**) and mixed equimolar NaCl + Phe solution (

**b**). Markers indicate the experimental data. Lines indicate the results of simulations carried out for δ = 400 μm (solid lines) and for δ = 50 μm (dashed lines). Other parameters for calculations correspond to conditions of the experiment (Table A1, Appendix A).

**Figure 4.**The pH of individual NaCl and mixed NaCl + Phe solutions (

**a**), and concentrations of phenylalanine species (mixed solution) in the D circuit vs. time of ND process (

**b**). Markers indicate the experimental data. Lines indicate the results of simulations carried out for δ = 400 μm (solid lines) and for δ = 50 μm (dashed lines). Other parameters for calculations correspond to conditions of the experiment (Table A1, Appendix A).

**Figure 5.**The time required to reduce the concentration of Na

^{+}and Cl

^{−}ions in the desalination circuit by 50%, as well as the ion transfer coefficients for CEM and AEM vs. DBL thickness. Calculations are made for ND desalination of a mixed NaCl + Phe solutions. Parameters for calculations are presented in Table A1, Appendix A.

Membranes | MK-40_{prof} | MA-40_{prof} |
---|---|---|

Maximum ^{1} thickness in swollen state (cm) | 0.065 ± 0.0005 [22] | 0.059 ± 0.0005 |

Minimum ^{2} thickness in swollen state (cm) | 0.030 ± 0.0005 | 0.030 ± 0.0005 |

Water content (wt %) | 42 ± 1 [22] | 44 ± 2 |

Ion-exchange capacity (meq cm^{−3} wet membrane) | 1.7 ± 0.1 [22] | 2.4 ± 0.1 |

Electric conductivity in 0.1 M NaCl (S m^{−1}) | 0.58 [22] | 0.39 [41] |

^{1}The membrane thickness between the smooth surface and the top of the profile on the profiled surface.

^{2}The membrane thickness between the smooth surface and the bottom of the profile on the profiled surface.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kozmai, A.; Goleva, E.; Vasil’eva, V.; Nikonenko, V.; Pismenskaya, N.
Neutralization Dialysis for Phenylalanine and Mineral Salt Separation. Simple Theory and Experiment. *Membranes* **2019**, *9*, 171.
https://doi.org/10.3390/membranes9120171

**AMA Style**

Kozmai A, Goleva E, Vasil’eva V, Nikonenko V, Pismenskaya N.
Neutralization Dialysis for Phenylalanine and Mineral Salt Separation. Simple Theory and Experiment. *Membranes*. 2019; 9(12):171.
https://doi.org/10.3390/membranes9120171

**Chicago/Turabian Style**

Kozmai, Anton, Elena Goleva, Vera Vasil’eva, Victor Nikonenko, and Natalia Pismenskaya.
2019. "Neutralization Dialysis for Phenylalanine and Mineral Salt Separation. Simple Theory and Experiment" *Membranes* 9, no. 12: 171.
https://doi.org/10.3390/membranes9120171